That is fucking ridiculous (not saying it's illegal, just ridiculous). The DJ paid fees to be able to play the music, and they expect the restaurant to also pay fees?
I stopped reading after this because you didn't follow the link or read the text. The DJ paid the same fee you do for a CD. Period. End of story. (S)He may have paid for the PA equipment as well. That has absolutely nothing to do with the fact that someone is using this for entertainment in his place of business as a way to encourage more business.
[Having now taken the moment to read your piss poor analogy, let me throw a more apt one at you]
It's more like if I write a book and then someone creates a movie from that book, should I have a right to proceeds from the movie? According to your analogy, I should just get nothing because the movie studio bought a single copy of my book, even though now, billions could have my story out there and, to many of them, a book that a movie they've seen isn't worth reading, so I shouldn't make money off of them.
I don't for a second believe that the DJ actually paid the fees, in fact, it seems the owner merely assumed (s)he did. And even if (s)he did, (s)he did so for performance within (her/)his own venue, as it's how (her/)his business has to be run. A restaurant owner who ignores this cost of doing business should get sued. The sad part is, it appears that this particular situation only came about because this owner refuses to be educated on his responsibilities and decided that settling didn't make sense. Hell, it seems like he didn't even seek out legal advice.